Find the median of 17, 26, 60, 45, 33, 32, 29, 34 and 56. If 26 is replaced by 62, what will be the new median ?

On arranging the given set of data in ascending order of magnitude, we get: 17, 26, 29, 32, 33, 34, 45, 56 and 60.

Number of observations, n = 9 (odd)

Median = $\big(\dfrac{n + 1}{2}\big)^{\text{th}} \text{ term}$

= $\big(\dfrac{9 + 1}{2}\big)^{\text{th}} \text{ term}$

= $\big(\dfrac{10}{2}\big)^{\text{th}} \text{ term}$

= 5th term

Thus, Median = 33

Now, replacing 26 with 62, the new set of numbers is : 17, 62, 60, 45, 33, 32, 29, 34 and 56.

On arranging these new numbers in ascending order, we get: 17, 29, 32, 33, 34, 45, 56, 60 and 62.

Number of observations, n = 9 (odd)

Median = $\big(\dfrac{n + 1}{2}\big)^{\text{th}} \text{ term}$

= $\big(\dfrac{9 + 1}{2}\big)^{\text{th}} \text{ term}$

= $\big(\dfrac{10}{2}\big)^{\text{th}} \text{ term}$

= 5th term

Thus, Median = 34

Hence, the original median is 33 and the new median after replacing 26 with 62 is 34.